Technical Field
The present disclosure relates generally to the field of electromagnetic well logging techniques. More specifically, the present disclosure relates to providing improved inversion techniques for determining characteristics of a subsurface formation based on electromagnetic measurements obtained using a well logging tool disposed in a borehole.
Background Information
This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the subject matter described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, not as admissions of prior art.
Logging tools have long been used in wellbores to make, for example, formation evaluation measurements to infer properties of the formations surrounding the borehole and the fluids in the formations. As examples only, common logging tools include electromagnetic tools, nuclear tools, and nuclear magnetic resonance (NMR) tools. Electromagnetic logging tools typically measure the resistivity (or its reciprocal, conductivity) of a formation. For instance, such electromagnetic resistivity tools include galvanic tools, induction tools, and propagation tools. Typically, a measurement of the attenuation and phase shift of an electromagnetic signal that has passed through the formation is used to determine the resistivity and/or other characteristics of the formation.
The concept of multiaxial (e.g., triaxial) electromagnetic measurements can be traced back to the 1960s, with the concept having been described in U.S. Pat. No. 3,014,177 to Hungerford. Since then, various triaxial electromagnetic tools have been introduced. See, e.g., Kriegshäuser et al., “A New Multicomponent Induction Logging Tool to Resolve Anisotropic Formations,” Transactions of the SPWLA 41st Annual Logging Symposium, Paper D (2000). For instance, triaxial electromagnetic tools may include a multiarray electromagnetic induction tool having collocated transmitter and/or receiver coils, such as of a type described generally in Barber et al., “Determining Formation Resistivity In The Presence of Invasion,” SPE 90526, presented at the SPE Annual Technical Conference and Exhibition, Houston, Tex., Sep. 26-29, 2004, or in Rosthal et al., “Field Test Results of an Experimental Fully-Triaxial Induction Tool,” Transactions of the SPWLA 44th Annual Logging Symposium, Paper QQ (2003). Additional multi-array triaxial induction tools continue to be developed. See, e.g., Hou et al., WO Patent Publication No. WO2011/123379A1; see also Hou et al., “Real-time Borehole Correction For a New Multicomponent Array Induction Logging Tool in OBM Wells,” Transactions of the SWPLA 42th Annual Logging Symposium, Paper PPP (2012).
When compared to certain older conventional tools, some of the more recent electromagnetic tools include those that incorporate mutually orthogonal coils and/or tilted coils to the tool design, which can serve as a transmitter, a receiver, or both (e.g., a transceiver). The incorporation of such coils with off-borehole axis orientation enables measuring a full, a nearly full, or a partially full tensor measurement instead of, for example, just a zz-component, as would be the case in some conventional tools with off-borehole axis coil arrangements. Such an expanded set of measurements may allow for extraction of resistivity anisotropy and geometry of subsurface formations. For example, multiaxial electromagnetic logging instruments can also be used to determine the relative dip angle (θ) and dip azimuth angle (Φ) of rock formations as well as anisotropic formation resistivities, including vertical resistivity (Rv) and horizontal resistivity (Rh). The apparent conductivity tensor measured by triaxial electromagnetic tools is sensitive to these formation parameters.
Several methods are known for solving for such formation parameters, each having certain advantages and disadvantages. For instance, one category of these methods is based on a formation model where bed boundaries are neglected, and a uniform anisotropic formation model is assumed. This is sometimes referred to as a 0D (zero-D) inversion or a 0D formation model. Example implementations of 0D models are described in more detail in commonly owned International Patent Application Publication No. WO2011/091216, which is hereby incorporated by reference in its entirety. Some advantages of 0D inversions are that they are computationally fast and thus are often suitable for use as a real-time answer product for generating coarse estimates of formation properties, and that they generally provide high-resolution dip estimation. 0D inversions can provide good results when used in formations with weak resistivity contrast and/or a slow varying resistivity. However, when the resistivity contrast in a given formation is large, 0D inversion algorithms may be negatively impacted by shoulder bed effects (e.g., bed boundary effects), as 0D formations models can be considered “simplified” in the sense that they do not include bed boundaries in the formation model. This can result in inaccuracies and adverse effects on both resistivity and dip estimations.
To overcome the shoulder bed effect, bed boundaries may be incorporated in the formation model. The simplest formation model that accounts for shoulder bed effects is a 1D formation model (e.g., based on vertical 1D algorithm). The basic assumption of a 1D formation model is that dip and azimuth are constant across the whole model, although resistivity (Rh and Rv) may vary from bed to bed. In other words, for a 1D model, each bed is assigned a different anisotropy characterized by horizontal resistivity (Rh) and vertical resistivity (Rv), with all the bed boundaries are assumed to be parallel to each other. The normal to the bedding plane is allowed to be tilted relative to the borehole axis. Accordingly, the resultant orientation is characterized by formation dip and dip azimuth.
These parameters can be recovered with a 1D inversion for petrophysical and geological applications. When applied to actual data, the corresponding depth zone is segmented first into a number of small subzones for the ease of 1D inversion implementation. 1D inversion is run over all subzones sequentially first, and the inversion results from all subzones are then combined as the final results for the whole depth zone. Each of these subzones is referred to as an inversion zone, or an inversion window. For example, an inversion zone with a length of up to 100 ft has been reported to be used for some 1D inversion methods. It is also noted that 1D inversions are also relatively fast from a computational standpoint and thus can be used for real-time or near/substantially real-time applications (providing of results without an appreciable delay). Thus, from an industry perspective, 1D inversion techniques are generally considered as a suitable tradeoff between the model fitness (e.g., compared to 0D inversion techniques) and computational cost. Examples of 1D inversion techniques are described in Wang et al., “Triaxial Induction Logging: Theory, Modeling, Inversion, and Interpretation,” SPE 103897, SPE International Oil & Gas Conference and Exhibition, Dec. 5-7, 2006.
However, as the use of triaxial electromagnetic logging has increased in popularity, field data sets have shown that formations are often not 1D in the real world. Rather, variations in dip and azimuth are often observed over the length of a given inversion zone. Such variations violate the assumptions of a 1D formation model, and thus indicate that in principle, 1D formation models may not be the best choice for modeling these so-called complex formations. Further, in extreme cases, variation of dip and dip azimuth in the formation may lead to large model errors in the data, which may translate to large errors in resistivity calculations and dip estimates obtained using 1D inversions.
One way of overcoming the drawbacks of 1D inversions in complex formations is to use even higher-dimension inversions, such as 3D inversions which are capable of modeling earth formations even more accurately. As will be appreciated, 3D inversions have been applied in processing cross-well electromagnetic measurements and for controlled source electromagnetic measurements in marine environments. In theory, higher-dimension inversions, such as a 3D inversion, often provide more accurate data by reducing or eliminating model errors. However, from a practical standpoint, such methods are generally time-consuming and require vast computing resources and processing capabilities which generally render them unsuitable for providing real-time or near real-time data and answer products. Furthermore, the inevitable increase in the number of unknowns makes the inversion overall more difficult due to non-uniqueness issues (e.g., can result in multiple models that fit the data).